If you have some free time before arriving in Kutaisi, open the map of Kutaisi in Russian and consider which district of Kutaisi to stay in — left bank or right bank. If you are primarily interested in city attractions, it is better to stay in the city center.
Perhaps you are in the mood to travel outside the city and visit nearby villages? Then check the map of Kutaisi, select the areas of the city from which it will be more convenient to travel to the target attractions, and look at the map of Kutaisi with hotels. There are hotels, guesthouses, and hostels in almost every area of the city.